Relationship of IRR to ROI on a Level Term Life Insurance Policy

[Pages:4]Article from:

Product Matters!

June 2013 ? Issue 86

Relationship of IRR to ROI on a

Level Term Life Insurance Policy

By Wayne Stuenkel

Wayne Stuenkel, FSA, CERA, MAAA, is senior vice president

& chief actuary at Protective Life Corp in Birmingham, Ala. He can be reached at Wayne.Stuenkel@

.

O ne of the primary pricing measures for individual life insurance products is the internal rate of return on a statutory basis. The internal rate of return (IRR) for a policy is a single interest rate that discounts all policy cash flows back to the issue date of the policy, such that the sum of discounted cash flows equals zero. "Cash flows" include statutory income, taxes, required capital, and imputed interest on required capital. An insurer will often require that products be priced to achieve a certain minimum IRR threshold.

Additionally, many companies report annual earnings on a GAAP basis. As a by-product of preparation of GAAP income, an annual return on GAAP investment (ROI) at the line of business level or the product level can be calculated. A GAAP ROI calculation typically includes GAAP income plus imputed interest on required capital in the numerator, and required capital plus stat/GAAP differences (DAC, reserves, taxes) in the denominator.

A recurring question from those who look at product profitability concerns the relationship of lifetime IRR to annual ROI. Some observers (often including insurance company CEOs) expect that the annual ROI for a product should be equal in all years to the lifetime IRR for the product, assuming that product assumptions (lapse, mortality, interest rate, etc.) are met. However, in practice, annual ROI never seems to be equal to lifetime IRR, even if product assumptions are met.

Several excellent papers have been written which examine the relationship between lifetime statutory IRR and annual GAAP ROI. Especially notable in this regard are papers written by Brad Smith (TSA 39, pp. 257-293) and Bob Beal (NAAJ Volume 4, Number 4, pp. 1-11). However, neither of these papers specifically identified those product variables that cause annual ROI to vary from the lifetime IRR.

So that we could more fully understand the relationship between IRR and ROI, we constructed a term life insurance product. The product provides a level amount of insurance for 20 years, in exchange for equal annual premium payments for 20 years. At the end of 20 years, all policies lapse without value, while the product continues as a whole life product with a high guaranteed

premium rate. There are no cash values or dividends. This product is generally consistent with products that are currently being sold; however, it is constructed for the purpose of demonstrating the relationship of IRR and ROI, and does not duplicate the products sold by our company or any other company.

The product was constructed in a spreadsheet for ease of manipulation, and therefore includes several simplifying assumptions (annual premiums and expenses at the start of the policy year, death claims and lapses at the end of the policy year, etc.) The spreadsheet was used to calculate the lifetime statutory IRR and the annual GAAP ROI assuming that all experience emerges exactly as expected.

We found that it is possible to construct a hypothetical product such that expected annual GAAP ROIs are level and equal to the lifetime statutory IRR. The assumptions and methodologies for this product are shown in Appendix A.

However, some of the assumptions and methodologies that are necessary to produce expected level

18 | June 2013 | Product Matters!

annual ROIs equal to lifetime IRR are either actuarially unsound or outside of statutory and GAAP accounting conventions. The assumptions and methodologies that are necessary to produce level annual ROIs equal to lifetime IRR include:

? DAC interest rate equal to IRR rate ? No required capital based on assets, reserves, or

insurance inforce net of reserves ? No DAC tax ? Statutory reserves equal to GAAP reserves ? GAAP reserve mortality equal to pricing mortality ? GAAP reserve interest rate equal to pricing

earned interest rate ? Lapse rate for GAAP reserves and DAC amorti-

zation equal to pricing lapse rate

In this article, we will refer to the variables above as the "slope-introducing variables," or SIVs.

It was interesting to observe which of the assumptions and methodologies, while changing the level of ROI and IRR, did not affect the relationship of ROI to IRR. These assumptions included:

? Premium rate per thousand and policy size ? Slope and level of mortality rates ? Lapse rates--both absolute level and pattern (so

long as GAAP = pricing) ? Earned interest rate on required capital ? Tax rate ? Reinsurance (if the form is coinsurance) ? Commissions and expenses (both direct and

ceded) ? Required capital based on direct premiums

To examine the effect of the SIVs, we constructed a hypothetical product that had a level ROI that was equal to IRR. (To produce a level ROI that was equal to IRR, the SIVs were set at a level which was either actuarially unsound or outside of accounting conventions.) We then changed each SIV individually to a setting that is typically found in practice, and observed the effect of the change in the SIV on the relationship of ROI to IRR.

The different patterns of ROI that we observed when the SIVs were changed to more typical settings were as follows:

Appendix A

Illustrative Assumptions for Level Term Product "Slope-Introducing Variables" are those Italicized Assumptions for which "Typical" Setting is

Different from "Level ROI" Setting

Variable

Setting for "Level ROI=IRR" * "Typical" Setting

Premium rate Earned interest rate Tax rate Lapse rate (pricing, GAAP) DAC tax rate

$0.80/M/year 7.00% 35.00% 12, 11, 10, 9, 8, 7, 6...... 0.00%

Same Same Same Same 7.70% of net consideration

Pricing mortality Direct commission + expense Reinsurance percentage Reinsurance method Reinsurance allowance

45% of 1975-80 S&U

Same

190% (1), 10% (2-10), 4% (11+) Same

90%

Same

Coinsurance

Same

100% (1), 50% (2-10), 12% (11+) Same

GAAP reserve interest rate GAAP reserve mortality GAAP reserve method Statutory reserve interest rate Statutory reserve mortality

Same as earned rate Same as pricing mortality Net level Same as GAAP rate Same as GAAP mortality

95% of earned rate 105% of pricing mortality Same 4.00% 100% of 1980 CSO

Statutory reserve method

Same as GAAP method

CRVM ? segmented or unitary (minimum ? cx mean reserve)

RBC - % of direct premium

3.40%

Same

RBC - % of net reserves

0.00%

2.76%

RBC - % of net inforce

0.000%

0.136%

DAC interest rate

Equal to IRR rate

7.00%

*Variables that are not "slope-introducing variables" can be set at any level. Setting at a level different than shown will change the level of ROI and IRR, but not the relationship between ROI and IRR.

? "Positive sloping ROI," defined as ROIs that are lower than IRR in the early durations, then rise to be greater than IRR in later durations, was observed when (a) the DAC interest rate was set lower than the IRR rate, (b) GAAP reserve mortality was higher than pricing mortality, or (c) GAAP reserve interest rate was less than pricing earned interest rate.

CONTINUED ON PAGE 20

Product Matters! | June 2013 | 19

Relationship of IRR to ROI ... | from page 19

Appendix B

Illustrative Results for Level Term Product

(1) Statutory Lifetime Internal Rate of Return

"Level ROI = IRR" setting 19.1%

"Typical" setting (stat reserves = segmented) 11.4%

"Typical" setting (stat reserves = unitary) 15.3%

Duration

(2) Annual GAAP Return on Investment

"Level ROI = IRR" setting

"Typical" setting (stat reserves = segmented)

"Typical" setting (stat reserves = unitary)

1

19.1%

13.1%

13.1%

2

19.1%

13.2%

13.2%

3

19.1%

12.1%

13.6%

4

19.1%

11.3%

14.0%

5

19.1%

10.8%

14.7%

6

19.1%

10.5%

16.1%

7

19.1%

10.3%

19.0%

8

19.1%

10.3%

26.4%

9

19.1%

10.3%

75.2%

10

19.1%

10.5%

Undefined

11

19.1%

10.3%

Undefined

12

19.1%

10.3%

Undefined

13

19.1%

10.2%

Undefined

14

19.1%

10.2%

Undefined

15

19.1%

10.3%

Undefined

16

19.1%

10.3%

Undefined

17

19.1%

10.4%

Undefined

18

19.1%

10.6%

60.2%

19

19.1%

10.9%

24.9%

20

19.1%

11.4%

16.2%

*"Undefined" means that numerator of ROI calculation is positive, but denominator is negative

? "Negative sloping ROI," defined as ROIs that are greater than IRR in the early durations, then decline to be less than IRR in later durations, was observed when (a) DAC tax was used or (b) required capital based on reserves, assets, or inforce net of reserves and reinsurance was used.

? The effect of statutory reserves on the slope of ROI depended on the statutory reserving method. Using reserves that are typical of XXX product designs (segmented reserves, no deficiencies) produces a negatively sloping ROI. Using reserves that were typical of unitary product designs (single-segment reserves, no deficiencies) produces a positively sloping ROI.

The largest effects on ROI slope arose from the DAC interest rate (positive slope), DAC tax (negative slope), and statutory reserve (both slopes) variables. When we combined all of the assumptions, we found that the product ROI had a generally positive slope for unitary products, and a generally negative slope for XXX products. The slopes of both types of products would become more positive if the loading of GAAP reserve mortality over pricing mortality were increased, or if the reduction in the GAAP reserve interest rate from the pricing earned interest rate were increased. The IRRs and ROIs for the tested variables are displayed in Appendix B.

Based on our work, we believe that it is impossible for the annual GAAP ROI for level term life insurance policies to be level and equal to IRR. Even if a company perfectly met all of its pricing assumptions, we believe that certain assumptions and methodologies that are required either by accounting convention or by sound actuarial practice introduce a slope to the pattern of annual GAAP ROIs.

We would be interested to know whether other actuaries have performed similar calculations on other types of business.

20 | June 2013 | Product Matters!

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